For any ordinal of uncountable cofinality, a -tree is a tree of height such that for each , where . In this note we get a Pressing Down Lemma for -trees and discuss some of its applications. We show that if is an uncountable ordinal and is a Hausdorff tree of height such that for each , then the tree is collectionwise Hausdorff if and only if for each antichain and for each limit ordinal with , is not stationary in . In the last part of this note, we investigate some...
This paper focuses on the multi-objective filtering of multirate time-varying systems with random sensor saturations, where both the variance-constrained index and the index are employed to evaluate the filtering performance. According to address issues, the high-frequency period of the internal state of the system is nondestructively converted to the low-frequency period, which determined by the measurement devices. Then the saturated output of multiple sensors is modeled as a sector bounded...
The past decades have witnessed several well-known beautiful conclusions on four con-cyclic points. With highly promising research value, we profoundly studied circumscribed ellipses of convex quadrilaterals in this paper. Using tools of parallel projective transformation and analytic geometry, we derived several theorems including the proof of the existence of circumscribed ellipses of convex quadrilaterals, the properties of its minimal coverage area, and locus center, respectively. This simple...
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